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Proof

(2005)

99 min. Miramax. Directors: Quentin Tarantino, Robert Rodriguez. Cast: Danny Trejo, Rose McGowan, Freddy Rodriguez, Josh Brolin, Marley Shelton.

Some things cannot be proven or disproven—trust, faith, love, sanity, and the meaning of existence. This oh-so-popular postmodern theme spawned the Pulitzer-Prize-winning play of 2001, David Auburn's Proof (also, in its way, this year's Pulitzer winner for drama, John Patrick Shanley's Doubt). Auburn, in collaboration with Rebecca Miller, has adapted Proof for the screen, and if the just-so package wrapped by Miramax's Harvey Weinstein (and reuniting Shakespeare in Love's director John Madden and star Gwyneth Paltrow) reveals less than its trimmings promise, it's still a thoughtful and useful gift.

Madden and Paltrow also collaborated on a London stage production of Proof, and their confidence brings clarity to the material while draining it of some of its spontaneity. Paltrow plays Catherine, devoted daughter to a genius mathematician named Robert (Anthony Hopkins). When Robert's brilliance dulls with the advance of age, mental instability emerges and effectively ends his academic career at the University of Chicago. Catherine puts her life on hold to care for her father and, day by day, share his hope of reclaiming his once-great mind.

Robert's story unfolds in flashback scenes, underscoring the looming shadow cast by genius and familial authority. At the film's outset, Catherine and her sister Claire (Hope Davis) must deal with the practical and emotional fallout of his recent death. The long-distant Claire sees Robert's death as an opportunity to end a messy chapter of her family history and forestall a new and equally tragic chapter from beginning. Claire believes that Catherine shares their father's potential for genius and insanity. In a gesture of newfound responsibility (and assertion of control), Claire insists on relocating her sister from the haunted university home to a protective environment.

Naturally, Claire's plan is cause for considerable tension, in part because of Catherine's personal incompatibility with her fussy sister and in part because of Catherine's considerable self-doubt. As Catherine faces the ever-more-likely prospect of being locked outside of the world she shared with her father and the world she desires for herself, grief begins to look a lot like insanity. Ground zero is the arcane and mysterious field of mathematics. In Robert's declining years, he enjoys a period of resurgence and believes he's on the cusp of a major breakthrough; meanwhile, Catherine explores her own potential as a graduate student in mathematics. Certainly, she is her father's daughter, but will she reveal his genius, his insanity, or both?

A fourth character shows a vested interest in the answer to that question. Hal (Jake Gyllenhaal), a doctoral student once under Robert's mentorship, reveals two not unrelated desires upon his death: to fulfill his long-held longing for Catherine and to plumb Robert's ostensibly crazed scribblings for signs of brilliance. As the dust clears, a key piece of evidence appears: a mathematical proof that, should it check out, will prove to be a major advance. Catherine claims to have authored the proof; Hal insists it could only be the work of her father.

The cast acquits itself admirably, though Paltrow and Hopkins come to the fore: the former enjoying a well-rounded character and the latter responding to juicy theatrics. Davis earnestly does her best with her brittle role; Gyllenhaal's equivocal lover, puppyish and ambitious in equal measure, never fully coalesces, but the script and director share responsibility. In the central role, Paltrow successfully anchors the film, but proves emblematic of the film's ineffable failure to be thrillingly superb: too often, she seems to wear her trauma like a Greek mask.

Auburn's story sparks intriguing considerations about greatness—so powerfully seductive and so terribly elusive—and the far edges of reason that yield to genius and madness. The screenplay's complex but never confusing structure intensifies interest and holds at bay the inevitable disapointment of resolution. From the first scene to the last, this phase of Catherine's life is a proof: she reviews it for verification, looks for a more direct path, a "better" way, but concludes that it is what it is. Proof plays cleverly with the arcane mysteries of game theory, and if it's only a game, happily, it's one worthy of exhibition. In the end, Auburn and Miller invite reflection on an epochal question: do our lives add up to something?